Rewrite as a simplified fraction. ${0.7\overline{34} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 734.3434...\\ 10x &= 7.3434...\end{align*}}$ Subtracting the two equations, we have: ${990x = 727}$ ${x = \dfrac{727}{990}} $